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<li class="navelem"><a class="el" href="dir_d8a420a1774de8c3d9c51191947d11dc.html">initBounValProbs</a></li><li class="navelem"><a class="el" href="dir_0d59a952f2f6d268d914532b382e0335.html">CahnHilliard_AllenCahn</a></li><li class="navelem"><a class="el" href="dir_d6c0cfcda9f36aaba255415a575e6f84.html">2D_bsplines_B2</a></li>  </ul>
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<div class="title">bsplines.h</div>  </div>
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<a href="bsplines_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="preprocessor">#ifndef bsplines_H</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="preprocessor"></span><span class="preprocessor">#define bsplines_H</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="preprocessor"></span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="preprocessor">#include &lt;vector&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="preprocessor">#include &lt;string&gt;</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="preprocessor">#include &lt;fstream&gt;</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="preprocessor">#include &lt;iostream&gt;</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"><a class="line" href="classbsplines.html">    8</a></span>&#160;<span class="keyword">class </span><a class="code" href="classbsplines.html">bsplines</a>{</div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;</div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160; <span class="keyword">public</span>:</div>
<div class="line"><a name="l00011"></a><span class="lineno"><a class="line" href="classbsplines.html#a4fd93b4086aab71baf2db0ddd528718c">   11</a></span>&#160;  <a class="code" href="classbsplines.html#a4fd93b4086aab71baf2db0ddd528718c">bsplines</a>(){};</div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;  <span class="keywordtype">void</span> <a class="code" href="classbsplines.html#ab9e3ccb3022c9ece5f4c08eb9ee3d29a">reinit</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> p_,</div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;          std::vector&lt;std::vector&lt;double&gt; &gt; X_,</div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;          std::vector&lt;std::vector&lt;double&gt; &gt; CPts_);</div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;</div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;  <span class="keywordtype">void</span> <a class="code" href="classbsplines.html#ab9e3ccb3022c9ece5f4c08eb9ee3d29a">reinit</a>(std::string fname);</div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;  <span class="comment">/*</span></div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="comment">  template&lt;typename T,typename U&gt;</span></div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="comment">  auto divZeroSafe(T a,U b);</span></div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="comment">  template&lt;typename T&gt;</span></div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="comment">  T N_ip (unsigned int i, unsigned int j, unsigned int P, T x);</span></div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="comment">  template&lt;typename T&gt;</span></div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;<span class="comment">  T dkN_dxk (unsigned int k, unsigned int i, unsigned int j, unsigned int P, T x);</span></div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="comment">  */</span></div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;  <span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;  <span class="keywordtype">void</span> <a class="code" href="classbsplines.html#a746ccab89b99102d98050ec3c863e22f">eval</a>(<span class="keyword">const</span> std::vector&lt;T&gt; &amp;x,</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;        T &amp;y,</div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;        std::vector&lt;T&gt; &amp;dy_dx,</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;        std::vector&lt;std::vector&lt;T&gt; &gt; &amp;ddy_dxdx);</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160; <span class="keyword">private</span>:</div>
<div class="line"><a name="l00034"></a><span class="lineno"><a class="line" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">   34</a></span>&#160;  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>;</div>
<div class="line"><a name="l00035"></a><span class="lineno"><a class="line" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">   35</a></span>&#160;  std::vector&lt;std::vector&lt;double&gt; &gt; <a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>;</div>
<div class="line"><a name="l00036"></a><span class="lineno"><a class="line" href="classbsplines.html#a4f52ee262089428974c98a746b2418ad">   36</a></span>&#160;  std::vector&lt;std::vector&lt;double&gt; &gt; <a class="code" href="classbsplines.html#a4f52ee262089428974c98a746b2418ad">CPts</a>;</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;};</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;</div>
<div class="line"><a name="l00039"></a><span class="lineno"><a class="line" href="classbsplines.html#ab9e3ccb3022c9ece5f4c08eb9ee3d29a">   39</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="classbsplines.html#ab9e3ccb3022c9ece5f4c08eb9ee3d29a">bsplines::reinit</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> p_,</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;                 std::vector&lt;std::vector&lt;double&gt; &gt; X_,</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;                 std::vector&lt;std::vector&lt;double&gt; &gt; CPts_){</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;  <a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a> = p_;</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;  <a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a> = X_;</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;  <a class="code" href="classbsplines.html#a4f52ee262089428974c98a746b2418ad">CPts</a> = CPts_;</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;  </div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;}</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;</div>
<div class="line"><a name="l00049"></a><span class="lineno"><a class="line" href="classbsplines.html#a3117ee78d14ff7267b67311ed3e6b2a0">   49</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="classbsplines.html#ab9e3ccb3022c9ece5f4c08eb9ee3d29a">bsplines::reinit</a>(std::string fname){</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;  <span class="comment">//Read in knot vectors and control points</span></div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> m, n;</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;  <span class="keywordtype">char</span> c; <span class="comment">//To catch the # sign in the header</span></div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;  <span class="keywordtype">double</span> d;</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;  std::ifstream file;</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;  std::string filename = fname+<span class="stringliteral">&quot;Cpts.txt&quot;</span>;</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;  file.open(filename);</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;  file &gt;&gt; c;</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;  file &gt;&gt; <a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>; file &gt;&gt; m; file &gt;&gt; n;</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;  <a class="code" href="classbsplines.html#a4f52ee262089428974c98a746b2418ad">CPts</a>.resize(m,std::vector&lt;double&gt;(n));</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;  <span class="keywordflow">for</span>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;m; ++i){</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;    <span class="keywordflow">for</span>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j=0; j&lt;n; ++j){</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;      file &gt;&gt; d;</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;      <a class="code" href="classbsplines.html#a4f52ee262089428974c98a746b2418ad">CPts</a>[i][j] = d;</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;    }</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;  }</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;  file.close();</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;  filename = fname+<span class="stringliteral">&quot;knots.txt&quot;</span>;</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;  file.open(filename);</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;  file &gt;&gt; c;</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;  file &gt;&gt; <a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>; file &gt;&gt; m; file &gt;&gt; n;</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;  <a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>.resize(2);</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;  <a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>[0].resize(m);</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;  <a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>[1].resize(n);</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;  <span class="keywordflow">for</span>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;m; ++i){</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;      file &gt;&gt; d;</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;      <a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>[0][i] = d;</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;  }</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;  <span class="keywordflow">for</span>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;n; ++i){</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;    file &gt;&gt; d;</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;    <a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>[1][i] = d;</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;  }</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;  file.close();</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;}</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;<span class="comment">/*</span></div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;<span class="comment">template&lt;typename T,typename U&gt;</span></div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;<span class="comment">auto bsplines::divZeroSafe(T a,U b){</span></div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;<span class="comment">  if(b==0){ return 0.*a; }</span></div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;<span class="comment">  else{ return a/b; }</span></div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;<span class="comment">}</span></div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;<span class="comment">template&lt;typename T&gt;</span></div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;<span class="comment">T bsplines::N_ip (unsigned int i, unsigned int j, unsigned int P, T x){</span></div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;<span class="comment">  T N;</span></div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;<span class="comment">  if(P == 0){</span></div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;<span class="comment">    N = (X[j][i] &lt;= x &amp;&amp; x &lt; X[j][i+1]);</span></div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;<span class="comment">  }</span></div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;<span class="comment">  else{</span></div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;<span class="comment">    N = (x - X[j][i])*divZeroSafe(N_ip(i,j,P-1,x),X[j][i+P] - X[j][i]) +</span></div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;<span class="comment">      (X[j][i+P+1] - x)*divZeroSafe(N_ip(i+1,j,P-1,x),(X[j][i+P+1] - X[j][i+1]));</span></div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;<span class="comment">  }</span></div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;<span class="comment">  return N;</span></div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;<span class="comment">}</span></div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;<span class="comment">template&lt;typename T&gt;</span></div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;<span class="comment">T bsplines::dkN_dxk (unsigned int k, unsigned int i, unsigned int j, unsigned int P, T x){</span></div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;<span class="comment">  // k^th derivative at knot i, poly. order P, evaluated at variable x_j = x</span></div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;<span class="comment">  T dkNdxk;</span></div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;<span class="comment">  if (k == 0){</span></div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;<span class="comment">    dkNdxk = N_ip(i,j,P,x);</span></div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;<span class="comment">  }</span></div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;<span class="comment">  else if(P == 0){</span></div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;<span class="comment">    dkNdxk = 0.;</span></div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;<span class="comment">  }</span></div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;<span class="comment">  else{</span></div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;<span class="comment">    dkNdxk = P*divZeroSafe(dkN_dxk(k-1,i,j,P-1,x),X[j][i+P] - X[j][i]) -</span></div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;<span class="comment">      P*divZeroSafe(dkN_dxk(k-1,i+1,j,P-1,x),(X[j][i+P+1] - X[j][i+1]));</span></div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;<span class="comment">  }</span></div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;<span class="comment">  return dkNdxk;</span></div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;<span class="comment">}</span></div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;<span class="comment">template&lt;typename T&gt;</span></div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;<span class="comment">void bsplines::eval(const std::vector&lt;T&gt; &amp;x,</span></div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;<span class="comment">            T &amp;y,</span></div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;<span class="comment">            std::vector&lt;T&gt; &amp;dy_dx,</span></div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;<span class="comment">            std::vector&lt;std::vector&lt;T&gt; &gt; &amp;ddy_dxdx){</span></div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;<span class="comment">  y = 0.;</span></div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;<span class="comment">  dy_dx.resize(2,0.);</span></div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;<span class="comment">  ddy_dxdx.resize(2,std::vector&lt;T&gt;(2,0.));</span></div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;<span class="comment">  unsigned int n1 = X[0].size()-p-1;</span></div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;<span class="comment">  unsigned int n2 = X[1].size()-p-1;</span></div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;<span class="comment">  for(unsigned int j=0; j&lt;n1; ++j){</span></div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;<span class="comment">    for(unsigned int k=0; k&lt;n2; ++k){</span></div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;<span class="comment">      y += CPts[j][k]*N_ip(j,0,p,x[0])*N_ip(k,1,p,x[1]);</span></div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;<span class="comment">      dy_dx[0] += CPts[j][k]*dkN_dxk(1,j,0,p,x[0])*dkN_dxk(0,k,1,p,x[1]);</span></div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;<span class="comment">      dy_dx[1] += CPts[j][k]*dkN_dxk(0,j,0,p,x[0])*dkN_dxk(1,k,1,p,x[1]);</span></div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;<span class="comment">      ddy_dxdx[0][0] += CPts[j][k]*dkN_dxk(2,j,0,p,x[0])*dkN_dxk(0,k,1,p,x[1]);</span></div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;<span class="comment">      ddy_dxdx[1][1] += CPts[j][k]*dkN_dxk(0,j,0,p,x[0])*dkN_dxk(2,k,1,p,x[1]);</span></div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;<span class="comment">      ddy_dxdx[0][1] += CPts[j][k]*dkN_dxk(1,j,0,p,x[0])*dkN_dxk(1,k,1,p,x[1]);</span></div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;<span class="comment">    }</span></div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;<span class="comment">  }</span></div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;<span class="comment">  ddy_dxdx[1][0] = ddy_dxdx[0][1];</span></div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;<span class="comment">}</span></div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;<span class="comment">*/</span></div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;<span class="comment">// Evaluate splines using de Boors&#39; algorithm from de Boor, &quot;On Calculating with B-Splines&quot;, 1972.</span></div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00152"></a><span class="lineno"><a class="line" href="classbsplines.html#a746ccab89b99102d98050ec3c863e22f">  152</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="classbsplines.html#a746ccab89b99102d98050ec3c863e22f">bsplines::eval</a>(<span class="keyword">const</span> std::vector&lt;T&gt; &amp;x,</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;            T &amp;y,</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;            std::vector&lt;T&gt; &amp;dy_dx,</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;            std::vector&lt;std::vector&lt;T&gt; &gt; &amp;ddy_dxdx){</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;  <span class="comment">// First find out in which knot span the point x is located</span></div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i, j, n = <a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>[0].size();</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> k=0; k&lt;n-1; ++k){</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;    <span class="comment">//std::cout &lt;&lt; k &lt;&lt; &quot; &quot; &lt;&lt; X[0][k] &lt;&lt; std::endl;</span></div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;    <span class="keywordflow">if</span> ((x[0] &gt;= <a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>[0][k]) &amp;&amp; (x[0] &lt; <a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>[0][k+1])){</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;      i = k;</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;      <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;    }</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;  }</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;  n = <a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>[1].size();</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> k=0; k&lt;n-1; ++k){</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;    <span class="comment">//std::cout &lt;&lt; k &lt;&lt; &quot; &quot; &lt;&lt; X[1][k] &lt;&lt; std::endl;</span></div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;    <span class="keywordflow">if</span> ((x[1] &gt;= <a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>[1][k]) &amp;&amp; (x[1] &lt; <a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>[1][k+1])){</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;      j = k;</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;      <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;    }</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;  }</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;  <span class="comment">//std::cout &lt;&lt; &quot;i: &quot; &lt;&lt; i &lt;&lt; &quot;, j: &quot; &lt;&lt; j &lt;&lt; std::endl;</span></div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;  <span class="comment">//Now, compute all necessary basis functions</span></div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;  std::vector&lt;std::vector &lt;T&gt; &gt; N1(<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>+1,std::vector&lt;T&gt;(<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>+1,0.)), N2(<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>+1,std::vector&lt;T&gt;(<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>+1,0.));</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;  std::vector&lt;T&gt; DP1(<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>,0.), DM1(<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>,0.), DP2(<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>,0.), DM2(<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>,0.);</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;  N1[0][0] = 1.;</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;  N2[0][0] = 1.;</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;  T M1, M2;</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> s=0; s&lt;<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>; ++s){</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;    DP1[s] = <a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>[0][i+s+1]-x[0];</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;    DM1[s] = x[0] - <a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>[0][i-s];</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;    DP2[s] = X[1][j+s+1]-x[1];</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;    DM2[s] = x[1] - X[1][j-s];</div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;    N1[0][s+1] = 0;</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;    N2[0][s+1] = 0; <span class="comment">//11*p-1 to here</span></div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> r=0; r&lt;=s; ++r){</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;      M1 = N1[r][s]/(DP1[r]+DM1[s-r]); <span class="comment">//3</span></div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;      N1[r][s+1] += DP1[r]*M1; <span class="comment">//3</span></div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;      N1[r+1][s+1] = DM1[s-r]*M1; <span class="comment">//4</span></div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;      M2 = N2[r][s]/(DP2[r]+DM2[s-r]); <span class="comment">//3</span></div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;      N2[r][s+1] += DP2[r]*M2; <span class="comment">//3</span></div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;      N2[r+1][s+1] = DM2[s-r]*M2; <span class="comment">//4, 21*p*(p+1)/2</span></div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;    }</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;  } <span class="comment">//Total flop count to this point: //21*p*(p+1)/2 + 11*p - 1</span></div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;  <span class="comment">//Evaluate the function and derivatives</span></div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;  y = 0.;</div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;  dy_dx.resize(2,0.);</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;  ddy_dxdx.resize(2,std::vector&lt;T&gt;(2,0.));</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> r1=0; r1&lt;p+1; ++r1){</div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> r2=0; r2&lt;p+1; ++r2){</div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;      y += <a class="code" href="classbsplines.html#a4f52ee262089428974c98a746b2418ad">CPts</a>[r1+i-<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>][r2+j-<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>]*N1[r1][<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>]*N2[r2][<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>]; <span class="comment">//7*(p+1)*(p+1) + p*p</span></div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;    }</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;  }</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> r1=1; r1&lt;p+1; ++r1){</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> r2=0; r2&lt;p+1; ++r2){</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;      dy_dx[0] += p*(<a class="code" href="classbsplines.html#a4f52ee262089428974c98a746b2418ad">CPts</a>[r1+i-<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>][r2+j-<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>]-<a class="code" href="classbsplines.html#a4f52ee262089428974c98a746b2418ad">CPts</a>[r1+i-p-1][r2+j-<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>])/(<a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>[0][r1+i]-<a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>[0][r1+i-p])*N1[r1-1][p-1]*N2[r2][<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>]; </div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;      dy_dx[1] += p*(<a class="code" href="classbsplines.html#a4f52ee262089428974c98a746b2418ad">CPts</a>[r2+i-<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>][r1+j-<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>]-<a class="code" href="classbsplines.html#a4f52ee262089428974c98a746b2418ad">CPts</a>[r2+i-<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>][r1+j-p-1])/(<a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>[1][r1+j]-<a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>[1][r1+j-p])*N1[r2][<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>]*N2[r1-1][p-1]; <span class="comment">//40*p*(p+1) + p*(p-1)</span></div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;    }</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;  }</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> r1=1; r1&lt;p+1; ++r1){</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> r2=1; r2&lt;p+1; ++r2){</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;      ddy_dxdx[0][1] += p*p*(<a class="code" href="classbsplines.html#a4f52ee262089428974c98a746b2418ad">CPts</a>[r1+i-<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>][r2+j-<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>]-<a class="code" href="classbsplines.html#a4f52ee262089428974c98a746b2418ad">CPts</a>[r1+i-p-1][r2+j-<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>]-<a class="code" href="classbsplines.html#a4f52ee262089428974c98a746b2418ad">CPts</a>[r1+i-<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>][r2+j-p-1]+<a class="code" href="classbsplines.html#a4f52ee262089428974c98a746b2418ad">CPts</a>[r1+i-p-1][r2+j-p-1])/(<a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>[0][r1+i]-<a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>[0][r1+i-p])/(<a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>[1][r2+j]-<a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>[1][r2+j-<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>])*N1[r1-1][p-1]*N2[r2-1][p-1]; <span class="comment">//42*p*p + (p-1)*(p-1)</span></div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;    }</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;  }</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> r1=2; r1&lt;p+1; ++r1){</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> r2=0; r2&lt;p+1; ++r2){</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;      ddy_dxdx[0][0] += p*(p-1)*(<a class="code" href="classbsplines.html#a4f52ee262089428974c98a746b2418ad">CPts</a>[r1+i-p][r2+j-p]-2*<a class="code" href="classbsplines.html#a4f52ee262089428974c98a746b2418ad">CPts</a>[r1+i-p-1][r2+j-p]+<a class="code" href="classbsplines.html#a4f52ee262089428974c98a746b2418ad">CPts</a>[r1+i-p-2][r2+j-p])/(<a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>[0][r1+i]-<a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>[0][r1+i-<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>])/(<a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>[0][r1+i-1]-<a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>[0][r1+i-p])*N1[r1-2][p-2]*N2[r2][<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>]; </div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;      ddy_dxdx[1][1] += p*(p-1)*(<a class="code" href="classbsplines.html#a4f52ee262089428974c98a746b2418ad">CPts</a>[r2+i-p][r1+j-p]-2*<a class="code" href="classbsplines.html#a4f52ee262089428974c98a746b2418ad">CPts</a>[r2+i-p][r1+j-p-1]+<a class="code" href="classbsplines.html#a4f52ee262089428974c98a746b2418ad">CPts</a>[r2+i-p][r1+j-p-2])/(<a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>[1][r1+j]-<a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>[1][r1+j-<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>])/(<a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>[1][r1+j-1]-<a class="code" href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">X</a>[1][r1+j-p])*N1[r2][<a class="code" href="classbsplines.html#a792fef4919ad545581902926c8d43b60">p</a>]*N2[r1-2][p-2]; <span class="comment">//72*(p+1)*(p-1) + p*(p-2)</span></div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;    }</div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;  }</div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;  ddy_dxdx[1][0] = ddy_dxdx[0][1];</div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;} <span class="comment">// total: 165*p*p + 70*p ...</span></div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;<span class="preprocessor">#endif //bsplines_H</span></div>
<div class="ttc" id="classbsplines_html_a4fd93b4086aab71baf2db0ddd528718c"><div class="ttname"><a href="classbsplines.html#a4fd93b4086aab71baf2db0ddd528718c">bsplines::bsplines</a></div><div class="ttdeci">bsplines()</div><div class="ttdef"><b>Definition:</b> bsplines.h:11</div></div>
<div class="ttc" id="classbsplines_html_a4180c283b106ed5356a6f22b0f867451"><div class="ttname"><a href="classbsplines.html#a4180c283b106ed5356a6f22b0f867451">bsplines::X</a></div><div class="ttdeci">std::vector&lt; std::vector&lt; double &gt; &gt; X</div><div class="ttdef"><b>Definition:</b> bsplines.h:35</div></div>
<div class="ttc" id="classbsplines_html"><div class="ttname"><a href="classbsplines.html">bsplines</a></div><div class="ttdef"><b>Definition:</b> bsplines.h:8</div></div>
<div class="ttc" id="classbsplines_html_a4f52ee262089428974c98a746b2418ad"><div class="ttname"><a href="classbsplines.html#a4f52ee262089428974c98a746b2418ad">bsplines::CPts</a></div><div class="ttdeci">std::vector&lt; std::vector&lt; double &gt; &gt; CPts</div><div class="ttdef"><b>Definition:</b> bsplines.h:36</div></div>
<div class="ttc" id="classbsplines_html_a746ccab89b99102d98050ec3c863e22f"><div class="ttname"><a href="classbsplines.html#a746ccab89b99102d98050ec3c863e22f">bsplines::eval</a></div><div class="ttdeci">void eval(const std::vector&lt; T &gt; &amp;x, T &amp;y, std::vector&lt; T &gt; &amp;dy_dx, std::vector&lt; std::vector&lt; T &gt; &gt; &amp;ddy_dxdx)</div><div class="ttdef"><b>Definition:</b> bsplines.h:152</div></div>
<div class="ttc" id="classbsplines_html_a792fef4919ad545581902926c8d43b60"><div class="ttname"><a href="classbsplines.html#a792fef4919ad545581902926c8d43b60">bsplines::p</a></div><div class="ttdeci">unsigned int p</div><div class="ttdef"><b>Definition:</b> bsplines.h:34</div></div>
<div class="ttc" id="classbsplines_html_ab9e3ccb3022c9ece5f4c08eb9ee3d29a"><div class="ttname"><a href="classbsplines.html#ab9e3ccb3022c9ece5f4c08eb9ee3d29a">bsplines::reinit</a></div><div class="ttdeci">void reinit(unsigned int p_, std::vector&lt; std::vector&lt; double &gt; &gt; X_, std::vector&lt; std::vector&lt; double &gt; &gt; CPts_)</div><div class="ttdef"><b>Definition:</b> bsplines.h:39</div></div>
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